<!DOCTYPE html>
<html>
<!--
Copyright 2007 The Closure Library Authors. All Rights Reserved.

Use of this source code is governed by an Apache 2.0 License.
See the COPYING file for details.
-->
<head>
<title>Closure Unit Tests - goog.math.Matrix</title>
<script src="../base.js"></script>
<script>
  goog.require('goog.math.Matrix');
  goog.require('goog.testing.jsunit');
</script>
</head>
<body>
<pre>
<script>

  function testConstuctorWithGoodArray() {
    var a1 = [ [1, 2], [2, 3], [4, 5] ];
    var m1 = new goog.math.Matrix(a1);
    assertArrayEquals('1. Internal array should be the same', m1.toArray(), a1);
    assertEquals(3, m1.getSize().height);
    assertEquals(2, m1.getSize().width);

    var a2 = [ [-61, 45, 123], [11112, 343, 1235] ];
    var m2 = new goog.math.Matrix(a2);
    assertArrayEquals('2. Internal array should be the same', m2.toArray(), a2);
    assertEquals(2, m2.getSize().height);
    assertEquals(3, m2.getSize().width);

    var a3 = [ [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4] ];
    var m3 = new goog.math.Matrix(a3);
    assertArrayEquals('3. Internal array should be the same', m3.toArray(), a3);
    assertEquals(4, m3.getSize().height);
    assertEquals(4, m3.getSize().width);
  }


  function testConstructorWithBadArray() {
    try {
      var m1 = new goog.math.Matrix([[1, 2, 3], [1, 2], [1]]);
    } catch (e) {
      assertNotNull('1. All arrays should be of equal length', e);
    }

    try {
      var m2 = new goog.math.Matrix([[1, 2], [1, 2], [1, 2, 3, 4]]);
    } catch (e) {
      assertNotNull('2. All arrays should be of equal length', e);
    }

    try {
      var m3 = new goog.math.Matrix([[1, 2], [1, 2], [1, 'a']]);
    } catch (e) {
      assertNotNull('3. Arrays should contain only numeric values', e);
    }

    try {
      var m4 = new goog.math.Matrix([[1, 2], [1, 2], [1, {a: 3}]]);
    } catch (e) {
      assertNotNull('4. Arrays should contain only numeric values', e);
    }

    try {
      var m5 = new goog.math.Matrix([[1, 2], [1, 2], [1, [1, 2, 3]]]);
    } catch (e) {
      assertNotNull('5. Arrays should contain only numeric values', e);
    }
  }


  function testConstructorWithGoodNumbers() {
    var m1 = new goog.math.Matrix(2, 2);
    assertEquals('Height should be 2', 2, m1.getSize().height);
    assertEquals('Width should be 2', 2, m1.getSize().width);

    var m2 = new goog.math.Matrix(4, 2);
    assertEquals('Height should be 4', 4, m2.getSize().height);
    assertEquals('Width should be 2', 2, m2.getSize().width);

    var m3 = new goog.math.Matrix(4, 6);
    assertEquals('Height should be 4', 4, m3.getSize().height);
    assertEquals('Width should be 6', 6, m3.getSize().width);
  }


  function testConstructorWithBadNumbers() {
    try {
      var m4 = new goog.math.Matrix(-4, 6);
    } catch (e) {
      assertNotNull('1. Negative argument should have errored', e);
    }

    try {
      var m5 = new goog.math.Matrix(4, -6);
    } catch (e) {
      assertNotNull('2. Negative argument should have errored', e);
    }

    try {
      var m6 = new goog.math.Matrix(4, 0);
    } catch (e) {
      assertNotNull('3. Zero argument should have errored', e);
    }

    try {
      var m7 = new goog.math.Matrix(0, 1);
    } catch (e) {
      assertNotNull('4. Zero argument should have errored', e);
    }
  }


  function testConstructorWithMatrix() {
    var a1 = [ [1, 2], [2, 3], [4, 5] ];
    var m1 = new goog.math.Matrix(a1);
    var m2 = new goog.math.Matrix(m1);
    assertArrayEquals(
        'Internal arrays should be the same', m1.toArray(), m2.toArray());
    assertNotEquals(
        'Should be different objects', goog.getUid(m1), goog.getUid(m2));
  }


  function testCreateIdentityMatrix() {
    var m1 = goog.math.Matrix.createIdentityMatrix(3);
    assertArrayEquals([[1, 0, 0], [0, 1, 0], [0, 0, 1]], m1.toArray());

    var m2 = goog.math.Matrix.createIdentityMatrix(4);
    assertArrayEquals(
        [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], m2.toArray());
  }


  function testIsValidArrayWithGoodArrays() {
    var fn = goog.math.Matrix.isValidArray;
    assertTrue('2x2 array should be fine', fn([[1, 2], [3, 5]]));
    assertTrue('3x2 array should be fine', fn([[1, 2, 3], [3, 5, 6]]));
    assertTrue(
        '3x3 array should be fine', fn([[1, 2, 3], [3, 5, 6], [10, 10, 10]]));
    assertTrue('[[1]] should be fine', fn([[1]]));
    assertTrue('1D array should work', fn([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]));
    assertTrue('Negs and decimals should be ok',
        fn([[0], [-4], [-10], [1.2345], [123.53]]));
    assertTrue('Hex, Es and decimals are ok', fn([[0x100, 10E-2], [1.213, 213]]));
  }


  function testIsValidArrayWithBadArrays() {
    var fn = goog.math.Matrix.isValidArray;
    assertFalse('Arrays should have same size', fn([[1, 2], [3]]));
    assertFalse('Arrays should have same size 2', fn([[1, 2], [3, 4, 5]]));
    assertFalse('2D arrays are ok', fn([[1, 2], [3, 4], []]));
    assertFalse('Values should be numeric', fn([[1, 2], [3, 'a']]));
    assertFalse('Values can not be strings', fn([['bah'], ['foo']]));
    assertFalse('Flat array not supported', fn([1, 2, 3, 4, 5]));
  }


  function testForEach() {
    var m = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    var count = 0, sum = 0, xs = '', ys = '';
    goog.math.Matrix.forEach(m, function(val, x, y) {
      count++;
      sum += val;
      xs += x;
      ys += y;
    });
    assertEquals('forEach should have visited every item', 9, count);
    assertEquals('forEach should have summed all values', 45, sum);
    assertEquals('Xs should have been visited in order', '000111222', xs);
    assertEquals('Ys should have been visited sequentially', '012012012', ys);
  }


  function testMap() {
    var m1 = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    var m2 = goog.math.Matrix.map(m1, function(val, x, y) {
      return val + 1;
    });
    assertArrayEquals([[2, 3, 4], [5, 6, 7], [8, 9, 10]], m2.toArray());
  }


  function testSetValueAt() {
    var m = new goog.math.Matrix(3, 3);
    for (var x = 0; x < 3; x++) {
      for (var y = 0; y < 3; y++) {
        m.setValueAt(x, y, 3 * x - y);
      }
    }
    assertArrayEquals([[0, -1, -2], [3, 2, 1], [6, 5, 4]], m.toArray());
  }


  function testGetValueAt() {
    var m = new goog.math.Matrix([[0, -1, -2], [3, 2, 1], [6, 5, 4]]);
    for (var x = 0; x < 3; x++) {
      for (var y = 0; y < 3; y++) {
        assertEquals(
            'Value at (x, y) should equal 3x - y',
            3 * x - y, m.getValueAt(x, y));
      }
    }
    assertNull('Out of bounds value should be null', m.getValueAt(-1, 2));
    assertNull('Out of bounds value should be null', m.getValueAt(-1, 0));
    assertNull('Out of bounds value should be null', m.getValueAt(0, 4));
  }


  function testSum1() {
    var m1 = new goog.math.Matrix([[1, 1, 1], [2, 2, 2], [3, 3, 3]]);
    var m2 = new goog.math.Matrix([[3, 3, 3], [2, 2, 2], [1, 1, 1]]);
    assertArrayEquals('Sum should be all the 4s',
        [[4, 4, 4], [4, 4, 4], [4, 4, 4]], m1.add(m2).toArray());
    assertArrayEquals('Addition should be commutative',
        m1.add(m2).toArray(), m2.add(m1).toArray());
  }


  function testSum2() {
    var m1 = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    var m2 = new goog.math.Matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]);
    assertArrayEquals('Sum should be all 0s',
        [[0, 0, 0], [0, 0, 0], [0, 0, 0]], m1.add(m2).toArray());
    assertArrayEquals('Addition should be commutative',
        m1.add(m2).toArray(), m2.add(m1).toArray());
  }


  function testSubtract1() {
    var m1 = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    var m2 = new goog.math.Matrix([[5, 5, 5], [5, 5, 5], [5, 5, 5]]);

    assertArrayEquals([[-4, -3, -2], [-1, 0, 1], [2, 3, 4]],
                      m1.subtract(m2).toArray());
    assertArrayEquals([[4, 3, 2], [1, 0, -1], [-2, -3, -4]],
                      m2.subtract(m1).toArray());
  }


  function testSubtract2() {
    var m1 = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    var m2 = new goog.math.Matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]);
    assertArrayEquals([[2, 4, 6], [8, 10, 12], [14, 16, 18]],
                      m1.subtract(m2).toArray());
    assertArrayEquals([[-2, -4, -6], [-8, -10, -12], [-14, -16, -18]],
                      m2.subtract(m1).toArray());
  }


  function testScalarMultiplication() {
    var m1 = new goog.math.Matrix([[1, 1, 1], [2, 2, 2], [3, 3, 3]]);
    assertArrayEquals(
        [[2, 2, 2], [4, 4, 4], [6, 6, 6]], m1.multiply(2).toArray());
    assertArrayEquals(
        [[3, 3, 3], [6, 6, 6], [9, 9, 9]], m1.multiply(3).toArray());
    assertArrayEquals(
        [[4, 4, 4], [8, 8, 8], [12, 12, 12]], m1.multiply(4).toArray());

    var m2 = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    assertArrayEquals(
        [[2, 4, 6], [8, 10, 12], [14, 16, 18]], m2.multiply(2).toArray());
  }


  function testMatrixMultiplication() {
    var m1 = new goog.math.Matrix([[1, 2], [3, 4]]);
    var m2 = new goog.math.Matrix([[3, 4], [5, 6]]);
    // m1 * m2
    assertArrayEquals([[1 * 3 + 2 * 5, 1 * 4 + 2 * 6],
                       [3 * 3 + 4 * 5, 3 * 4 + 4 * 6]],
                      m1.multiply(m2).toArray());
    // m2 * m1 != m1 * m2
    assertArrayEquals([[3 * 1 + 4 * 3, 3 * 2 + 4 * 4],
                       [5 * 1 + 6 * 3, 5 * 2 + 6 * 4]],
                      m2.multiply(m1).toArray());
    var m3 = new goog.math.Matrix([[1, 2, 3, 4],
                                   [5, 6, 7, 8]]);
    var m4 = new goog.math.Matrix([[1, 2, 3],
                                   [4, 5, 6],
                                   [7, 8, 9],
                                   [10, 11, 12]]);
    // m3 * m4
    assertArrayEquals([[1 * 1 + 2 * 4 + 3 * 7 + 4 * 10,
                        1 * 2 + 2 * 5 + 3 * 8 + 4 * 11,
                        1 * 3 + 2 * 6 + 3 * 9 + 4 * 12],
                       [5 * 1 + 6 * 4 + 7 * 7 + 8 * 10,
                        5 * 2 + 6 * 5 + 7 * 8 + 8 * 11,
                        5 * 3 + 6 * 6 + 7 * 9 + 8 * 12]],
                      m3.multiply(m4).toArray());
    assertThrows("Matrix dimensions should not line up.",
                 function () { m4.multiply(m3); });
  }

  function testMatrixMultiplicationIsAssociative() {
    var A = new goog.math.Matrix([[1, 2], [3, 4]]);
    var B = new goog.math.Matrix([[3, 4], [5, 6]]);
    var C = new goog.math.Matrix([[2, 7], [9, 1]]);

    assertArrayEquals('A(BC) == (AB)C',
                      A.multiply(B.multiply(C)).toArray(),
                      A.multiply(B).multiply(C).toArray());  
  }


  function testMatrixMultiplicationIsDistributive() {
    var A = new goog.math.Matrix([[1, 2], [3, 4]]);
    var B = new goog.math.Matrix([[3, 4], [5, 6]]);
    var C = new goog.math.Matrix([[2, 7], [9, 1]]);

    assertArrayEquals('A(B + C) = AB + AC',
                      A.multiply(B.add(C)).toArray(),
                      A.multiply(B).add(A.multiply(C)).toArray());

    assertArrayEquals('(A + B)C = AC + BC',
                      A.add(B).multiply(C).toArray(),
                      A.multiply(C).add(B.multiply(C)).toArray());
  }


  function testTranspose() {
    var m = new goog.math.Matrix([[1, 3, 1], [0, -6, 0]]);
    var t = [[1, 0], [3, -6], [1, 0]];
    assertArrayEquals(t, m.getTranspose().toArray());
  }


  function testAppendColumns() {
    var m = new goog.math.Matrix([[1, 3, 2], [2, 0, 1], [5, 2, 2]]);
    var b = new goog.math.Matrix([[4], [3], [1]]);
    var result = [[1, 3, 2, 4], [2, 0, 1, 3], [5, 2, 2, 1]];
    assertArrayEquals(result, m.appendColumns(b).toArray());
  }


  function testAppendRows() {
    var m = new goog.math.Matrix([[1, 3, 2], [2, 0, 1], [5, 2, 2]]);
    var b = new goog.math.Matrix([[4, 3, 1]]);
    var result = [[1, 3, 2], [2, 0, 1], [5, 2, 2], [4, 3, 1]];
    assertArrayEquals(result, m.appendRows(b).toArray());
  }


  function testSubmatrixByDeletion() {
    var m = new goog.math.Matrix([[1, 2, 3, 4], [5, 6, 7, 8],
        [9, 10, 11, 12], [13, 14, 15, 16]]);
    var arr = [[1, 2, 3], [5, 6, 7], [13, 14, 15]];
    assertArrayEquals(arr, m.getSubmatrixByDeletion_(2, 3).toArray());
  }


  function testMinor() {
    var m = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    assertEquals(-3, m.getMinor_(0, 0));
  }


  function testCofactor() {
    var m = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    assertEquals(6, m.getCofactor_(0, 1));
  }


  function testDeterminantForOneByOneMatrix() {
    var m = new goog.math.Matrix([[3]]);
    assertEquals(3, m.getDeterminant());
  }


  function testDeterminant() {
    var m = new goog.math.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
    assertEquals(0, m.getDeterminant()); 
  }


  function testGetSubmatrix() {
    var m = new goog.math.Matrix([[ 2, -1,  0, 1, 0, 0],
                                  [-1,  2, -1, 0, 1, 0],
                                  [ 0, -1,  2, 0, 0, 1]]);
    var sub1 = [[2, -1, 0], [-1, 2, -1], [0, -1, 2]];
    assertArrayEquals(sub1,
                      m.getSubmatrixByCoordinates_(0, 0, 2, 2).toArray()); 

    var sub2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];
    assertArrayEquals(sub2, m.getSubmatrixByCoordinates_(0, 3).toArray()); 
  }


  function testGetReducedRowEchelonForm() {
    var m = new goog.math.Matrix([[ 2, -1,  0, 1, 0, 0],
                                  [-1,  2, -1, 0, 1, 0],
                                  [ 0, -1,  2, 0, 0, 1]]);

    var expected = new goog.math.Matrix([[1, 0, 0, .75, .5, .25],
                                         [0, 1, 0, .5,  1,  .5 ],
                                         [0, 0, 1, .25, .5, .75]]);

    assertTrue(expected.equals(m.getReducedRowEchelonForm()));
  }


  function testInverse() {
    var m1 = new goog.math.Matrix([[ 2, -1,  0],
                                   [-1,  2, -1],
                                   [ 0, -1,  2]]);
    var expected1 = new goog.math.Matrix([[.75, .5, .25],
                                          [.5,  1,  .5 ],
                                          [.25, .5, .75]]);
    assertTrue(expected1.equals(m1.getInverse()));

    var m2 = new goog.math.Matrix([[4,  8],
                                   [7, -2]]);
    var expected2 = new goog.math.Matrix([[.03125,  .125 ],
                                          [.10936, -.0625]]);
    assertTrue(expected2.equals(m2.getInverse(), .0001));
  }


  function testEquals() {
    var a1 = new goog.math.Matrix([[1, 0, 0, .75, .5, .25],
                                   [0, 1, 0, .5,  1,  .5 ],
                                   [0, 0, 1, .25, .5, .75]]);

    var a2 = new goog.math.Matrix([[1, 0, 0, .75, .5, .25],
                                   [0, 1, 0, .5,  1,  .5 ],
                                   [0, 0, 1, .25, .5, .75]]);

    var a3 = new goog.math.Matrix([[1, 0, 0, .749, .5, .25],
                                   [0, 1, 0, .5,    1, .5 ],
                                   [0, 0, 1, .25,  .5, .75]]);

    assertTrue(a1.equals(a2));
    assertTrue(a1.equals(a3, .01));
    assertFalse(a1.equals(a3, .001));
  }

</script>

</body>
</html>
